As others have said, light and radio waves are both the same thing, and travel at the same speed, c. Electric energy travels at the speed of light through the wire, which is slower than c (about 1/3 c). The electrons themselves travel much, much slower, but their speed doesn’t really matter.
The reason light travels at the speed it does is that photons are massless, and from Einstein’s Special Relativity, we know that c is the only speed at which massless particles can move. The slower speed of light through a material is only an average speed: A photon will travel at c between the atoms, but when it hits an atom it will be briefly absorbed and then re-emitted, which takes time and on average slows it down.
Likewise, gravity is also predicted to propagate at c, and gravitons, if they exist, are massless. One can’t measure the speed of gravity from static masses, but if you move masses around, the gravitational field changes, and it takes the changes a while to reach distant points. These travelling changes in the gravitational field are gravitational waves, and a number of experiments are currently in progress to attempt to detect them.
That’s basically true, but it’s not a resonnance which is what I would think of when you say “at the right frequency.” While 2.4 GHz is pretty close to the peak in the curve of how much energy gets absorbed by water molecules, a microwave oven would work just fine pretty much anywhere between about 1 GHz and somewhere around 7 to 10 GHz, and its efficiency would slowly taper off as you got outside of those frequencies. It’s not “the right” frequency, it’s “somewhere in the right frequency band.”
Well, yeah. But it does nicely show the difference for a simple order of magnitude calculation. In other words, the radio waves are about ten to a hundred million times longer than visible light, so the visible photons have ten to a hundred million times more energy.
As for the electron motion issue, David Simmons gives a pretty good explanation. As soon as you set up a potential difference, you get an electric field, which propagates at the speed of light (this is roughly equivalent to the pressure wave). As a result, electrons feel the result almost instantaneously, no matter where in the conductor they are. It also helps to consider that, of course, the conductor is already full of electrons, so it’s not like the electrons at one end have to reach the other in order to feel the effect.
On preview: thanks for the correction, engineer_comp_geek I knew it was something like that, but I wasn’t sure exactly how it worked. I suppose I should have been less explicit in my choice of words.
No. As Ring hints at, the energy propagates outside the wire, and travels at the speed of light in the dielectric surrounding the wire. If the dielectric is air, that speed is almost equal to c. If the dielectric is say, polyethylene, the speed is about 2/3 c.
Yes.
This is simply wrong. The speed of light in a material medium is
u = permeability of the medium
e = permittivity of the medium
u[sub]0[/sub] = permeability of free space
u[sub]r[/sub] = relative permeability of the medium
e[sub]0[/sub] = permittivity of free space
e[sub]r[/sub] = relative permittivity of the medium
Now, u[sub]r[/sub] and e[sub]r[/sub] for copper are almost unity, so that the speed of light in copper is almost exactly equal to c.
As an example of a propagation velocity less than c, consider the polyethylene I referred to. For polyethylene, u[sub]r[/sub] = 2.3, u[sub]r[/sub] = 1.
The speed of transmission in bare copper wire surrounded by air is almost equal to the speed of light.
The speed of transmission in insulated copper wire is about equal to 8 or 9 inches/nanosecond as compared to just under 1 ft/nanosecond in air.
This is real good evidence that the speed of transmission is a function of the electromagnetic field surrounding the wire and not of the motion of the electrons in the wire.
When you shine a beam of light is the energy constantly being absorbed and re-emitted by all the air particles?
And if so, does this cause any changes in the way light functions? Besides the speed change, obviously. In other words would a beam of light act the same way in the vacuum of space as opposed to down here with all the atmospheric atoms floating aorund?
You sure about that? I’m pretty sure that the e[sub]r[/sub] for copper, or any conductor, is extremely high. So high that it’s assumed to be infinite in most calculations. I’m trying to find a reference…
Visible light has too low a frequency to excite the electrons in the molecules that make up the majority of air’s chemical composition. Molecular oxygen is transparent to 200nm and nitrogen to 170nm IIRC.
According to this Wikipedia article, it is the density of the medium that determines its refractive index (i.e. to what extent light is slowed down) if the light is not being absorbed.
If gravity propagated at a speed greater than c, wouldn’t it be possilble to change a gravitational field and detect the change miles away instantaneously, thus trasmitting information faster than c? Is this why people think the limit must be c?
In general relativity, gravity is shown to be a property of spacetime (that is, its curvature) and propagation occurs at a single speed for all fields. As I understand it, this speed not necessarily equal to c; however, it if goes slower then you have a potential for non-conservation of momentum, and if you go faster than light, it violates causality. The former is a stock principle of physics which gives every evidence of applying on all scales, from the cosmological to the quantum. The latter (causality) is something we’ve always assumed to be true, and while quantum mechanics offers a mechanism (entanglement) for connection between to non-adjacent points in spacetime (Einstein’s “spooky action at a distance.”) Irish physicist John Bell demonstrated that causality still holds despite instantaneous effect (i.e. one cannot transmit information via that connection). So there are reasons we don’t expect it to go any slower or faster than c, though those reasons are based upon assumptions, albeit assumptions that have proved true (or astoundlying accurate approximations) of our observations of the natural world.
So we don’t really have any expectation that gravity will propagate faster than c; to do so would through relativity and causality on the dole queue. We do expect it to travel uniformly at one speed, and our measurements show the speed as very near (and most likely equal to) c. If it doesn’t travel at c, we then need to come up with some explainations about how momentum is conserved in the propagating field (somehow) or let go of the otherwise indicated notion that momentum is conserved. Lord of Occam’s Razor obviously argues for s[sub]g[/sub] = c
I believe relativity is actually Chronos’ area of research, so maybe he can offer a more extensive explaination.
Thank you so much for showing me just how huge of a nerd I truly am. I started groaning, and my wife, who is certainly no dummy, looked at me like I was nuts. And SHE’s a nerd too!
I’m sorry but that is not correct. The reason I know this is a long time ago I worked out practically all the problems in Griffiths “Introduction to Electrodynamics” third edition and problem 9.18 is this one exactly.
Desmostylus in case you don’t want to wade through the above PDF the answer the author got is 403 m/s which is pretty close to my 400 m/s. The reason this is so different from your answer is that the velocity of propagation equals the wavelength times the frequency and although the frequency remains the same the wavelength changes dramatically.
Ring: The author of that page tosses off lines like: “The permeability of conductors is approximately that of vacuum.” Now, this is true of non-ferromagnetic conductors, but not true of a large and important class of conductors, i.e. those that are ferro-magnetic. So I ain’t takin’ this guy as gospel. I’ll look into it.
That certainly doesn’t surprise me. Considering how quickly the wave attenuates why would anyone care what its propagation velocity is? As far as I can see this stuff is only used to calculate skin depth and the reflection and transmission coefficients. But I’m no expert so these equations probably have all kind of uses of which I’m completely ignorant. I only used it as an example of why the EM energy must be transported in a wave outside the conductor.
Another thought: The electric field vector inside the conductor would point in the direction of current flow which means the Poynting vector would be perpendicular to the surface of the conductor. So this “inside the conductor wave” must be what causes the Ohmic heating?
But it does nicely show the difference for a simple order of magnitude calculation. In other words, the radio waves are about ten to a hundred million times longer than visible light, so the visible photons have ten to a hundred million times more energy.